If x = cos θ + i sin θ, then xⁿ + \(\frac { 1 }{ { x }^{ n } } \) is ______

If a = cos α + i sin α, b = -cos β + i sin β then \(\left( ab-\frac { 1 }{ ab } \right) \) is _________

If zⁿ = \(cos\frac { n\pi }{ 3 } +isin\frac { n\pi }{ 3 } \), then z₁, z₂ ..... z₆ is _________

The complex number z which satisfies the condition \(\left| \frac { 1+z }{ 1-z } \right| \) = 1 lies on _________

If z = \(\frac { 1 }{ 1-cos\theta -isin\theta } \), the Re(z) = ___________

If z = 1-cos θ + i sin θ, then |z| = _____________

If z = \(\frac { 1 }{ (2+3i)^{ 2 } } \) then |z| = ____________

The least positive integer n such that \(\left( \frac { 2i }{ 1+i } \right) ^{ n }\) is a positive integer is ____________

.If a = 3+i and z = 2-3i, then the points on the Argand diagram representing az, 3az and - az are _________

If a = cos θ + i sin θ, then \(\frac { 1+a }{ 1-a } \) = ___________

If \(\sqrt { a+ib } \)  = x + iy, then possible value of \(\sqrt { a-ib }\) is ___________

The value of (1+i) (1+i²) (1+i³) (1+i⁴) is ____________

If \(\omega =cis\cfrac { 2\pi }{ 3 } \), then the number of distinct roots of \(\left| \begin{matrix} z+1 & \omega & { \omega }^{ 2 } \\ \omega & z+{ \omega }^{ 2 } & 1 \\ { \omega }^{ 2 } & 1 & z+\omega \end{matrix} \right| \)=0

If \(\omega \neq 1\) is a cubic root of unity and \(\left| \begin{matrix} 1 & 1 & 1 \\ 1 & { -\omega }^{ 2 }-1 & { \omega }^{ 2 } \\ 1 & { \omega }^{ 2 } & { \omega }^{ 7 } \end{matrix} \right| \) = 3k, then k is equal to 

If \(\alpha \) and \(\beta \) are the roots of x²+x+1 = 0, then \({ \alpha }^{ 2020 }+{ \beta }^{ 2020 }\) is

If (1+i)(1+2i)(1+3i)...(1+ni) = x + iy, then \(2\cdot 5\cdot 10...\left( 1+{ n }^{ 2 } \right) \) is

The principal argument of \(\cfrac { 3 }{ -1+i } \) is

If z = x + iy is a complex number such that |z+2| = |z−2|, then the locus of z is

If z is a complex number such that \(z \in \mathbb{C} \backslash \mathbb{R}\) and \(z+\frac { 1 }{ z } \epsilon R\), then |z| is

The solution of the equation |z| - z = 1 + 2i is

If |z| = 1, then the value of \(\frac { 1+z }{ 1+\overline { z } }\) is

If |z - 2 + i | ≤ 2, then the greatest value of |z| is

If z is a non zero complex number, such that 2iz² = \(\bar { z } \) then |z| is

 The value of \(\sum_{n=1}^{13}\left(i^{n}+i^{n-1}\right)\) is